Detectors for high atomic number materials are used at shipping ports to search for radioactive and nuclear materials that may be hidden in shipping containers. In general, a shipping container may first pass through a radiation portal monitor, which is essentially a Geiger counter, to detect any unshielded nuclear matter, such as Uranium. However, lead and other dense materials can be used to smuggle radioactive and nuclear materials through radiation portal monitors by shielding the radioactive radiation emitted from the nuclear matter.
To detect Shielded Nuclear Material (SNM), the container may next pass through an X-ray detector. The X-ray detector is used to look for dense materials, such as lead, that may be in the shipping container. If the shipping container does not include a dense material, an X-ray image of the shipping container will be bright since the X-rays can pass through the goods in the shipping container. However, if the shipping container includes lead or other dense materials, the X-ray image will include a corresponding dark area since the X-rays cannot pass through the dense material. Thus, the detection of high-density materials by X-ray is an indicia that the shipping container contains SNM or other shielded contraband.
If the X-ray image provides such an indicia, the shipping container is taken to a muon scattering detector for further inspection. A muon scattering detector can be used to reconstruct a three-dimensional image of a volume, for example based on deflections and scattering angles of the muons as measured by planar detectors located above and below the shipping container. A threat detection algorithm can be used to automatically raise an alarm based on the resulting three-dimensional image.
Currently the information provided by the X-ray detector and the muon scattering detector is analyzed separately. It would be desirable to combine the information from the detectors to improve the sensitivity of the detection system.
The angular scattering of a muon as it transverses a thin layer of material of thickness L and scattering density λ, is conveniently described in terms of the scattering angle in a plane vertical to the layer. The average scattering angle is zero, and the distribution of scattering angles around this average can be approximated to a Gaussian distribution of width
      σ    =                            λ          ⁢                                          ⁢          L                            β        ⁢                                  ⁢        p              ,where β and p are the velocity of the muon as a fraction of the speed of light and the (magnitude of the) momentum of the muon. Over 95% of the scattering events are well described by this approximation. Since muons with energies below ˜0.3 GeV are unlikely to be measured, in practice the denominator is roughly equal to the momentum, and thus the muon's momentum sets the scale of the scattering. In addition to angular scattering, the muon may also be deflected to the sides by its interactions with the material. The muon momentum also sets the scale of such deflections, and of their correlations with the angular scattering.
The scattering density λ increases with the atomic number Z. A useful approximation is
      λ    =          C      ⁢              ρ        A            ⁢              (                  11.39          -                      ln            ⁢                                                  ⁢            Z                          )            ⁢              Z        ⁡                  (                      Z            +            1                    )                      ,where C is a constant, ρ is the mass density of the material, and A its atomic weight. For solids and liquids, ρ tends to grow together with A, though the correlation is a rough one. The mass of common cargos is dominated by elements with Z≥6, and of course Z≤94, so that the term in parenthesis changes slowly and λ increases almost as fast as Z2. Hence muon scattering is particularly sensitive to high-Z materials.
The expected energy loss of a muon as it passes a distance of Δx in a given material is ΔE=PsρΔx, where Ps is the stopping power of the material (the symbol
  dE  dxis often used in the literature instead of Ps) and ρ its mass density. The actual energy loss is distributed asymmetrically around this value, with a distribution often modeled by the Bethe-Bloch formula.